Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

typedef long long ll;
using namespace std;

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);

	cout.setf(std::ios_base::fixed,std::ios_base::floatfield);

	int n;cin >> n;
	int s[n];

	for (int i = 0;i < n;i++){
		cin >> s[i];
	}

	sort(s,s+n);

	double ans = -1;

	for (int c = 0;c < n;c++){
		for (int d = c;d < n;d++){
			if(c == d) continue;
			int a = -1, b= -1;
			for (int i = n-1;i >= 0;i--){
				if(i == c || i == d) continue;
				if(a == -1) a = i;
				else{ b = i; break;}
			}
			double val = (double)(s[a]+s[b])/(s[d]-s[c]);
			ans = max(ans,val);
		}
	}

	cout << ans << endl;

	return 0;

}